The Mössbauer Effect

In the case of the emission of x-rays from atoms, the recoil of the atom will shift the energy of the x-ray so that it is not reabsorbed. For some experiments it is useful to be able to measure the energy of the x-ray by reabsorbing it. One could move the detector at different velocities to find out when re-absorption was maximum and thus make a very accurate measurement of energy shifts. One example of this would be to measure the gravitational red (blue) shift of x-rays.

Mössbauer discovered that atoms in a crystal need not recoil significantly. In fact, the whole crystal, or at least a large part of it may recoil, making the energy shift very small. Basically, the atom emitting an x-ray is in a harmonic oscillator (ground) state bound to the rest of the crystal. When the x-ray is emitted, there is a good chance the HO remains in the ground state. An analysis shows that the probability is approximately

\begin{displaymath}\bgroup\color{black} P_0=e^{-E_{recoil}/\hbar\omega_{HO}} \egroup\end{displaymath}

Thus a large fraction of the radiation is emitted (and reabsorbed) without a large energy shift. (Remember that the crystal may have \bgroup\color{black}$10^{23}$\egroup atoms in it and that is a large number.

The Mössbauer effect has be used to measure the gravitational red shift on earth. The red shift was compensated by moving a detector, made from the same material as the emitter, at a velocity (should be equal to the free fall velocity). The blue shift was measured to be

\begin{displaymath}\bgroup\color{black} {\Delta\omega\over\omega}=(5.13\pm 0.51)\times 10^{-15} \egroup\end{displaymath}

when \bgroup\color{black}$4.92 \times 10^{-15}$\egroup was expected based upon the general principle of equivalence.

Jim Branson 2013-04-22